Related papers: American Options in the Hobson-Rogers Model
We consider the L\'evy model of the perpetual American call and put options with a negative discount rate under Poisson observations. Similar to the continuous observation case as in De Donno et al. [24], the stopping region that…
Financial markets tend to switch between various market regimes over time, making stationarity-based models unsustainable. We construct a regime-switching model independent of asset classes for risk-adjusted return predictions based on…
We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…
We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price $\pi$ is given…
It is well-known that using delta hedging to hedge financial options is not feasible in practice. Traders often rely on discrete-time hedging strategies based on fixed trading times or fixed trading prices (i.e., trades only occur if the…
This paper examines the valuation of American capped call options with two-level caps. The structure of the immediate exercise region is significantly more complex than in the classical case with constant cap. When the cap grows over time,…
In this paper we consider the following optimal stopping problem $$V^{\omega}_{\rm A}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process,…
We propose a continuous-time model of trading with heterogeneous beliefs. Risk-neutral agents face quadratic costs-of-carry on positions and thus their marginal valuations decrease with the size of their position, as it would be the case…
We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time $t_d$ during the lifetime of the option. The ex-dividend asset price process is…
Consider a discrete finite-dimensional, Markovian market model. In this setting, discretely sampled American options can be priced using the so-called ``non-recombining'' tree algorithm. By successively increasing the number of exercise…
We consider a mean-variance portfolio selection problem in a financial market with contagion risk. The risky assets follow a jump-diffusion model, in which jumps are driven by a multivariate Hawkes process with mutual-excitation effect. The…
The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and…
In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial…
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
Developments in finance industry and academic research has led to innovative financial products. This paper presents an alternative approach to price American options. Our approach utilizes famous \cite{heath1992bond} ("HJM") technique to…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
This paper examines a semi-analytical approach for pricing American options in time-inhomogeneous models characterized by negative interest rates (for equity/FX) or negative convenience yields (for commodities/cryptocurrencies). Under such…
Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the…
We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions,…